A theory has been developed to describe a heterogeneous, non equilibrium system in which diffusion, transport and chemical reaction are all occurring simultaneously. The variables entering the equations are: bead bound antigens, mobile antibodies that react specifically with the antigens but which have a distribution of rate and equilibrium constants for them, and mobile antigens which inhibit the antibody-bead bound antigen interaction. Characteristics of the affinity and rate constant distributions are related to characteristics of the elution profile by relatively simple expressions even for systems in which neither chemical equilibrium nor a local steady state has been established. The effect of movement in and out of the bead under non-ideal conditions (activity coefficient different from unity) is included. An important aspect of the development is the theoretical relation between the affinity of antibody for a surface bound antigen as opposed to the affinity for a free antigen. The theory suggests a method for obtaining the affinity constants for both reactions. Extensions and applications of a mathematical model of the hemolytic plaque assay continued. In addition, work was begun on the development of equations to be used in the quantitation of nonisotopic agglutination assays, which can be used as substitutes to radio immunoassay.